Friday, November 30, 2012

Predicting Regression in the 2013 NLL Season

In
sport, athletes can break past predictions either performing at
astronomical levels or competing below their projected skill level.When
given a proper sample size however, one can pick out
statistical anomalies as just that, a spike on the chart. As the laws of
regression tell us, most things will end up falling or rising closer to
the mean in the long run. This is true in lacrosse as shown by pal of
the blog Dan Shirley, who is totally serious and prefers to just be
called Dan.

The Math: He
took the data for players with 100+ shots from the years 2012, 2011,
and 2010. Next, He ran a regression with a constant of 0 for 2010 and
2011 eS% as the independent variables and 2012 as the dependent. This
basically means that it weights the 2010 and 2011 stats to find the best
weights to get 2012 results.The
formula would look like this: 2012_eS% = 2011_eS% * w1 + 2010_eS% * w2 +
c where year_eS% is the effective shooting percentage for that year and
w1/w2 are the weights from the regression and c is the linear constant
(0 in our case). So, with simplified numbers plugged in, we get 2012_eS%
= 2011_eS% * 0.71 + 2010_eS% * 0.31.As
an aside, the p-values (for alpha = 0.05) for the weights are 2011:
0.0288 and 2010: 0.3117. So it's technically not a super strong fit, but
who cares. I ran a regression for just one year predicting the next (ie
2011 -> 2012 and 2010 -> 2011) and came up with statistically
significant coefficients but that's more regression to the mean instead
of prediction. The main problem with that is it really hurts players
like JT who shoot REALLY well and it treats that as an outlier and
penalizes them the following year.Anyways...I
then took players that had 100+ shots in 2011 and 2012 and calculated
their 2013 eS%. I could do more, but players with over 100 shots are the
ones that are getting the majority of floor time and are the real
difference makers on offense.Here's
the results with the columns being: Player name, 2012 eS%, 2011 eS%,
Expected 2013 eS%, and change from 2012 (sorted from largest increase
(+) to largest decrease (-))

Player

2012

2011

E(x)

Delta
2012

Kevin
Buchanan

0.113

0.236

0.154

0.040

Aaron
Wilson

0.165

0.271

0.202

0.036

Chad Culp

0.245

0.323

0.274

0.029

Scott
Ranger

0.263

0.339

0.292

0.029

Stephan
Leblanc

0.246

0.315

0.272

0.026

Shawn
Williams

0.209

0.270

0.232

0.023

Cody
Jamieson

0.245

0.296

0.266

0.021

Dan
Dawson

0.263

0.312

0.284

0.021

Lewis
Ratcliff

0.242

0.288

0.261

0.019

Callum
Crawford

0.243

0.284

0.261

0.018

Rhys
Duch

0.282

0.315

0.298

0.016

Jeff
Shattler

0.286

0.316

0.301

0.015

Mike
Accursi

0.265

0.292

0.279

0.014

Ryan
Benesch

0.334

0.348

0.345

0.011

Ryan
Ward

0.276

0.287

0.285

0.009

Curtis
Dickson

0.318

0.323

0.326

0.008

Scott
Evans

0.238

0.247

0.245

0.008

Corey
Small

0.206

0.217

0.214

0.007

Drew
Westervelt

0.307

0.307

0.313

0.006

Dane
Dobbie

0.254

0.247

0.257

0.003

Luke
Wiles

0.321

0.307

0.323

0.002

Athan
Iannucci

0.263

0.247

0.263

0.000

Garrett
Billings

0.247

0.226

0.246

-0.002

Shawn
Evans

0.279

0.254

0.277

-0.002

Colin
Doyle

0.284

0.244

0.277

-0.007

Brendan
Mundorf

0.236

0.177

0.222

-0.014

John
Grant

0.290

0.211

0.271

-0.019

Josh
Sanderson

0.290

0.206

0.270

-0.021

John
Tavares

0.408

0.292

0.380

-0.028

Mark
Steenhuis

0.382

0.204

0.334

-0.048

You’ll see players like Kevin Buchanan, Aaron Wilson, Chad Culp, Scott
Ranger, and Stephan Leblanc score 4-6 more goals than last year and on the
other end John Grant, Josh Sanderson, John Tavares, and Mark Steenhuis score
3-7 fewer goals (based on if they take 150 shots.)